Curve path on sphere
You can try doing this:


Add the curve
Switch to edit mode and  subdivide the curve 4-5 times (press w to subdivide)
Add shrinkwrap modifier to the curve. Accept the default setting and as target set the sphere. Apply the modifier.
Now add the small sphere, with the array modifier and then the curve modifier with the settings you want (as done in the other blend file).


I am attaching the example blend.